conjugate module

If M is a right module over a ring R,
and α is an endomorphism of R,
we define the conjugate moduleMα
to be the right R-module
whose underlying set is {mα∣m∈M},
with abelian groupstructure identical to that of M
(i.e. (m-n)α=mα-nα),
and scalar multiplication given by
mα⋅r=(m⋅α⁢(r))α
for all m in M and r in R.